182:2.] on Mr, HerapatlCs Theory, 365 



the opposite direction. In any compound body, however, it is 

 only the superficial particles of the body the particles of the air 

 strike against ; and since the particles of the body are not fixed 

 to, but freely moving among, one another, except inasmuch as 

 they are prevented from flying off indefinitely by their mutual 

 attraction, the intensities of the colhsion between the particles 

 of the body and particles of the air are merely equal to what 

 would arise" if the former particles were free and disengaged, and 

 moving with the same velocity as the body of which they form a 

 part. These intensities, therefore, and the effect which they have 

 on the progress of the body, are by no means the same as they 

 would be if the particles of the body were firmly and inflexibly 

 united, or the body itself one perfect solid. Though this conse-. 

 quence is one of the most obvious that can be, C. has raised a 

 ** wonder how the cannon balls with their hard particles can get 

 on, when they strike the hard particles of the atmosphere in the 

 lines of their centres of gravity .'* Perhaps the greatest wonder 

 is, how so acute a reasoner as C. should have published an objec- 

 tion which evidently has no foundation to rest upon. 



After what I have shown of the merit and weight of C.'s 

 observations, and Mr. H.'s principles of colhsion, he will, per- 

 haps, take it kindly of me if I let alone his '' pin's head " diffi- 

 culty. I must confess I am very much disposed to obhge him ; 

 and, therefore, will leave the wisdom of one head to solve the 

 pha^nomena of the other. But I must beg leave to tell him that 

 Mr. Herapath had minutely considered this objection, and clearly 

 answered it in the very number of the Annals, and only five 

 pages after the Proposition from which C. would make us 

 believe he had the sagacity to draw it. Would C. have the 

 goodness to tell us whether the discovery of this consequence is 

 due to his own penetration ; or whether he has brought forward 

 the objection Mr. Herapath had himself raised, and artfully 

 omitted to notice Mr. H.'s explanation, for the purpose of 

 undermining a theory which prejudice would not allow him 

 to admit? Besides, what I have mathematically deduced in 

 Prop. C. Cor. 3, from the principles *' which," C. tells us, " are 

 as nearly as possible self-evident," Mr. Herapath has distinctly 

 shown, p. 292 and 293, Annals for April, 1821, *Uhatthe whole 

 difficulty of the case turns on the abstraction of the ideas of 

 magnitude and momentum." But I believe I have promised C. 

 not to pursue this part of his objections. I will, therefore, 

 desist. 



Prop. D. 



If two perfectly hard and equal balls come in contact, when 

 moving with equal momenta in the same right line towards oppo- 

 site parts, the intensity of the stroke as felt by each body in a 

 direction opposite to that in which it was moving, is equal to the 



